Oscillator Principles

Transcription

1 Oscillators

2 Introduction Oscillators are circuits that generates a repetitive waveform of fixed amplitude and frequency without any external input signal. The function of an oscillator is to generate alternating current or voltage waveforms. The only input to oscillator is the dc power supply Oscillator are used in radio, television, computers and communications. Oscillator can be viewed as a signal generator

3 Oscillator Principles An oscillator is a type of f/b amp. In which part of the o/p is f/b to the i/p via a feedback circuit. If the signal f/b is of proper magnitude & phase, the circuit produces alternating currents or voltages. Input voltage is zero (Vin0). The f/b is positive because most oscillator use positive f/b. 3

4 Oscillator Principles From the figure, Hence; v v + d v v f v in v f Bv 0 v 0 A v vd,, 0 v but v 0 and v 0 0 in A A v B Therefore Expressed in polar A v B in A v B o 0 or 360 o. The magnitude of the loop gain must be at least. The total phase shift of the loop gain must be equal to o o 0 or360 4

5 The types of Oscillator An oscillator is a circuit that produces a repetitive signal from a dc voltage. The feedback type oscillator which rely on a positive feedback of the output to maintain the oscillations. The relaxation oscillator makes use of an RC timing circuit to generate a non-sinusoidal signal such as square wave. 5

6 F/b type oscillator Vs relaxation oscillator Both use active (transistor, op-amp) and passive components (R,L,C) F/b type oscillator produces sine wave f/b determines the oscillation frequency Relaxation oscillator produces non-sinusoidal wave (square etc) use of an RC timing circuit to generate a nonsinusoidal signal 6

7 Feedback Oscillator Principles The feedback oscillator is widely used for generation of sine wave signals. The positive (in phase) feedback arrangement maintains the oscillations. The feedback gain must be kept to unity to keep the output from distorting. 7

8 Positive Feedback In-phase portion of the output voltage of an amplifier is fed back to the input with no net phase shift. V f - in-phase f/b voltage is amplified to produce the output voltage. The loop sustains the signal-produce continuous sinusoidal output voltage. This phenomenon is called oscillation. 8

9 Conditions for oscillation conditions Phase shift around the f/b loop 0 / 360 degree (the circuit must have a positive f/b) The loop gain, Acl must equal to (this condition called the Barkhausen Criterion) A cl A B V 9

10 Oscillators Types RC Oscillator - generate a sinusoidal waveform at a few Hz to khz range - Wien-bridge, the phase-shift, and the twin-t LC Oscillator - generate a sin wave at frequencies of 00 khz to 00 MHz - Colpitts, Clapp, Hartley, and Armstrong Crystal Oscillator - generate a square or sin wave over a wide range,i.e. about 0 khz to 30 MHz - more stable than RC & LC especially at high frequency 0

11 FEEDBACK OSCILLATORS: RC OSCILLATOR. Wien-bridge. Phase-shift 3. Twin-T

12 Oscillators With RC Feedback Circuits RC feedback oscillators are generally limited to frequencies of MHz or less. The types of RC oscillators that we will discuss are the Wien-bridge and the phase-shift.

13 . Wien-Bridge Oscillator 3

14 Cont Multiply the top and bottom by jωc, we get V V o jωc R ( + jωcr )( + jωcr ) + jωcr Divide the top and bottom by C R C R V V Now the amp gives o R C R C R C V 0 ' V K + jω RC + RC + R jω RC RC ' C ω Furthermore, for steady state oscillations, we want the feedback V to be exactly equal to the amplifier input, V. Thus V V V K o V o 4

15 Cont Hence K jωk R C R C Equating the real parts, R C R C R C R R C R C ω If R R R and C C C K 3 + C jω RC + RC + R jω RC RC 0 + C RC + RC + R jω RC RC ω RC K R C ω C + RC R C ω + R C f r πrc - Gain > 3 : growing oscillations - Gain < 3 : decreasing oscillations 5

16 Fundamental part of the Wien-Bridge Oscillator The lead-lag circuit of a Wien-bridge oscillator reduces the input signal by /3 and yields a response curve as shown. The frequency of resonance can be determined by the formula below. f r /πrc 6

17 Basic Circuit for Wien Bridge Oscillator The lead-lag circuit is in the positive feedback loop of Wienbridge oscillator. The voltage divider limits gain. The lead lag circuit is basically a band-pass with a narrow bandwidth. 7

18 Positive Feedback Condition Since there is a loss of about /3 of the signal in the positive feedback loop, the voltage-divider ratio must be adjusted such that a positive feedback loop gain of is produced. This requires a closed-loop gain of 3. The ratio of R and R can be set to achieve this. A cl B R /( R + R + R R R To achieved a Acl of 3 R R A cl R + R R ) 3 8

19 Start-Up Conditions To start the oscillations an initial gain greater than must be achieved. The back-to-back zener diode arrangement is one way of achieving this. When dc is first applied the zeners appear as opens. This allows the slight amount of positive feedback from turn on noise to pass. When dc power is first applied, the zener diode appears as open, thus R R R + R R 3 3 A cl R 3R + R R R R 3 9

20 Cont The lead-lag circuit narrows the feedback to allow just the desired frequency of these turn transients to pass. The higher gain allows reinforcement until the breakover voltage for the zeners is reached. 0

21 Cont Zener arrangement for gain control is simple but produces distortion because of the non-linearity of zener diodes. Automatic gain control (AGC) - maintain a gain of exact unity. A JFET in the negative feedback loop can be used to precisely control the gain. After the initial startup and the output signal increases the JFET is biased such that the negative feed back keeps the gain at precisely.

22 . Phase Shift Oscillator The phase shift oscillator utilizes three RC circuits to provide 80º phase shift that when coupled with the 80º of the opamp itself provides the necessary feedback to sustain oscillations. The gain must be at least 9 to maintain the oscillations. The frequency of resonance for the this type is similar to any RC circuit oscillator. The feedback, B is B 9 The frequency of oscillator, f r π 6RC

23 Cont The transfer function of the RC network is 3

24 Cont If the gain around the loop equals, the circuit oscillates at this frequency. Thus for the oscillations we want, Putting sjω and equating the real parts and imaginary parts, we obtain 4

25 Cont From equation () ; Substituting into equation () ; # The gain must be at least 9 to maintain the oscillations. 5

26 3. Twin-T Oscillator The twin-t types RC filters (LPF & HPF) used in feedback looputilizes a bandstop/notch arrangement of RC circuits to block all but the frequency of operation in the negative feedback loop. The only frequency allowed to effectively oscillate is the frequency of resonance, fr Oscillation only occur at fr where positive f/b through the voltage divider exist. Negative f/b is negligible. 6